1. Field of the Invention
The present invention relates to a musical tone synthesizing apparatus which is adaptable to an electronic musical instrument.
2. Prior Art
The conventionally known electronic musical instrument provides a waveform memory which pre-stores a musical tone waveform generated from a non-electronic musical instrument (hereinafter, simply referred to as "acoustic instrument") and the like. Then, the stored musical tone waveform is read from the waveform memory in response to an operation of a performer, so that a musical tone is to be generated based on the read musical tone waveform. In addition, the high-grade electronic musical instrument carries out certain operation on the read musical tone waveform, or executes the process of synthesizing plural musical tone waveforms. Thus, such high-grade electronic musical instrument can reproduce the musical tone with high fidelity.
Meanwhile, sounds actually generated by the above-mentioned acoustic instrument will be varied in accordance with the performance technique or environmental condition. In case of the wind instrument such as the clarinet, its musical tone waveform, even in the same scale, is varied in accordance with the blowing intensity, so that the audience can feel such variation of the generated musical tone waveform as the variation of tone color. This phenomenon will be explained later.
In order to reproduce the above-mentioned musical tone waveforms full of variety with high fidelity, the electronic musical instrument must provide the waveform memory capable of storing many kinds of waveforms and operation means capable of executing the complicated waveform processings. However, it is difficult to embody such electronic musical instrument based on the conventional techniques.
In order to overcome the above-mentioned difficulty, Japanese Patent Laid-Open Publication No. 63-40199 discloses another conventional instrument which models on the tone-generation mechanism of the acoustic instrument to thereby reproduce the musical tone generated by the the acoustic instrument without using the waveform memory.
Next, description will be given with respect to the simulation model of the acoustic instrument and the musical tone synthesizing apparatus using the simulation model in case of the wind instrument.
FIG. 1 shows the most simple model of the wind instrument consisting of a resonance tube 1 and a reed 2 made of elastic materials. When the performer blows his breath 2A into the reed 2, the reed 2 is bent due to breath pressure PA in the inside direction of the tube 1 (i.e., direction 2F). Since the reed 2 is elastic, the reed 2 is vibrated by the breath 2A. As a result, the pressure wave (i.e., compression wave) of air is produced in the inside of the tube 1 and reed 2. Then, such compression wave F progresses toward a terminal portion 1E of the tube 1. Thereafter, the progressive compression wave F is reflected by the terminal portion 1E so that reflected compression wave R is occurred. This reflected compression wave R is returned to the reed 2. Thus, the reed 2 is affected by pressure PR corresponding to the reflected compression wave R. As a result, the following pressure P is applied to the reed 2. EQU P=PA-PR (1)
Thus, the reed 2 vibrates in accordance with the above-mentioned pressure P and elastic characteristic thereof. FIG. 2 shows an example of the elastic characteristic of the reed 2, i.e., relation between the pressure P (i.e., INPUT) and displacement of the reed 2 (i.e., OUTPUT). As shown in FIG. 2, the displacement of the reed 2 varies in connection with the pressure with non-linear curve. If the pressure P reaches certain saturation level, the displacement of the reed 2 does not vary.
In the case where the vibration frequency of the reed 2 becomes equal to the resonance frequency of the tube 1 (which will be described later), the resonance phenomenon will occur so that the large compression wave is obtained from the tube 1. Due to such large compression wave, the wind instrument can produce the sound.
More specifically, in the case where the air vibration is occurred at the specific frequency (i.e., resonance frequency) determined by scale L of the air column of the tube 1, the standing wave of the air compression wave is produced in the direction of scale L (i.e., longitudinal direction of tube 1), so that the large vibration is obtained in the tube 1. This phenomenon is called as the foregoing "resonance phenomenon".
Next, description will be given with respect to the relation between the above-mentioned scale L of the tube 1 and wavelength of the standing wave. If both edges of the tube are open as shown in FIG. 3 so that the air particles can freely move at the edge portions of the tube, amplitudes of the compression waves F and R go maximum. In this case, the reflected compression wave R has the inverse phase of the progressive compression wave F at the terminal portion. Therefore, wavelength "w" of the standing wave which is produced in the tube 1 is indicated by the following formula (2). EQU w=2L/n (2)
, where n=1, 2, 3, . . . FIG. 3 shows three standing waves when n equals 1, 2, 3 respectively.
In contrast, when one edge of the tube is closed as shown in FIG. 4 so that the air particles cannot move at the closed edge portion of the tube, amplitudes of the compression waves F and R become zero. Therefore, wavelength w of the standing wave can be indicated by the following formula (3). EQU w=4L/(2n-1) (3)
, where n=1, 2, 3, . . . FIG. 4 shows three standing waves when n equals 1, 2, 3 respectively.
When the air vibration having resonance frequency fn (as indicated by the following formula (4)) is given to the tube 1 by the reed 2, the foregoing resonance phenomenon occurs in the tube 1. EQU fn=c/w (4)
, where c represents propagation velocity of the compression wave F, R.
Thereafter, since the reed 2 vibrates in synchronism with the standing wave in the tube 1, the resonance is maintained in the tube 1. More specifically, when the reed 2 is bent in direction 2F, the progressive compression wave F is produced. Then, this compression wave F is reflected by the terminal portion 1E so that the reflected compression wave R is produced. Thereafter, this reflected compression wave R bends the reed 2 in direction 2R (which is the inverse of the direction 2F) so that another progressive compression wave F is produced. This wave F is reflected by the terminal portion 1E and then returned to the reed 2. Therefore, another reflected compression wave R bends the reed 2 in direction 2F again. Thus, reed 2 continues to vibrate in synchronism with reciprocating motion of the compression wave (i.e., vibration of the standing wave).
As described heretofore, the reed 2 vibrates in synchronism with the standing wave of the compression wave in the tube 1 so that the resonance is maintained and consequently the wind instrument can generates the sound continuously. Herein, the reed 2 vibrates in non-linear manner, so that the compression waves F, R include higher harmonic components. In addition, the tube 1 has a plenty of different resonance frequencies as indicated in the foregoing formulae (2), (3). Thus, it is possible to obtain the air vibrations having different resonance frequencies in the tube 1.
FIG. 5 is a block diagram showing an electric configuration of the musical tone synthesizing apparatus which is obtained by simulating the tone-generation mechanism of the wind instrument as described heretofore. Incidentally, this configuration as shown in FIG. 5 is not limited to the wind instrument, but it is possible to apply this configuration to other instruments such as the string instrument.
In FIG. 5, 11 designates a non-linear element which simulates the operation of the reed 2, 12 designates a resonance circuit which simulates the tube 1, and 13 designates a subtractor which simulates the foregoing subtraction operation (1) which is applied to the reed 2. This subtractor 13 subtracts an output signal of the resonance circuit 12 (corresponding to the foregoing reflected compression wave R) from an input signal VA (corresponding to the foregoing breath pressure PA). Then, the subtraction result of the subtractor 13 is supplied to the non-linear element 11.
According to the configuration as shown in FIG. 5, DC bias is effected on the non-linear element 11 by the input signal VA. Then, the output of the non-linear element 11 is supplied to the resonance circuit 12. Thereafter, the output of the resonance circuit 12 is supplied to the non-linear element 11 via the subtractor 13, so that the non-linear element 11 is excited. Thus, the circuit shown in FIG. 5 carries out the oscillation operation.
Herein, the non-linear element 11 is designed such that its I/O characteristic will simulate the non-linear characteristic of the reed 2. This non-linear element 11 can be embodied by the known non-linear element such as the diode. Or, the non-linear element 11 can be embodied by a read-only memory (ROM) which stores the desirable non-linear function to be read out. As described above, the I/O characteristic of the non-linear element 11 can be designed to coincide with that of the reed. Thus, it is possible to obtain the output waveform of the non-linear element 11 which coincides with the vibration waveform of the reed.
FIGS. 6A-6I illustrate several vibration waveforms of the reed in the clarinet. As can be seen in the figures, strongly-performed tone and weakly-performed tone both belonging to the same musical scale have different vibration waveforms so that these tones are sounded in different tone colors in the wind instrument such as the clarinet. Herein, the vibration waveform of the weakly-performed tone is close to sine-waveform. On the other hand, the level of the vibration waveform of the strongly-performed tone is limited into the range defined by LL and LU which are determined by the elastic limit of the reed, so that the peak-portion of the vibration waveform of the strongly-performed tone must be distorted as compared to that of the sine-waveform. Such waveform distortion can be indicated by the variation of the output waveform of the non-linear element 11 whose bias-point is varied by the input signal VA corresponding to the breath pressure PA. In case of the weakly-performed tone, the bias-point of the non-linear element 11 is limited in certain linear range since the breath pressure PA is relatively small, so that the output signal of the non-linear element 11 has the waveform close to the sine-waveform. In case of the strongly-performed tone, the bias-point of the non-linear element 11 is in the non-linear range since the breath pressure PA is relatively large, so that the output signal of the non-linear element 11 has the waveform including a plenty of higher harmonic components.
Next, description will be given with respect to the resonance circuit 12 in detail. This resonance circuit 12 is designed to correspond to the shape of the resonance tube of the wind instrument to be simulated. FIG. 7 illustrates the transmission-frequency characteristic of the resonance tube of the clarinet, while FIG. 8 illustrates the transmission-frequency characteristic of the resonance tube of the oboe. As shown in FIGS. 7 and 8, the transmission-frequency characteristic of the tube of the wind instrument has a plenty of peak portions each corresponding to each of the resonance frequencies which are determined by the tube shape. Incidentally, the relation between the resonance frequency and tube shape can be indicated by the foregoing formulae (2), (3). Thus, the air vibration produced by the reed of each wind instrument is applied to the resonance tube, so that each wind instrument can generate the sound having the specific and unique tone color.
FIG. 9 illustrate the circuit which is obtained by simulating the transmission-frequency characteristic of the tube portion of the wind instrument. This circuit shown in FIG. 9 can be used as the foregoing resonance circuit 12 shown in FIG. 5. In FIG. 9, DF.sub.1 to DF.sub.n, DR.sub.1 to DR.sub.n designate delay circuits each configured by the multi-stage shift register (having three stages or more in general). These delay circuits simulate the transmission delay of the compression wave in the tube. Herein, the delay circuits DF.sub.1, DR.sub.n correspond to the tube portion which is the closest to the reed 2, while DF.sub.n, DR.sub.1 correspond to the tube portion which is the closest to the end portion 1E. The delay circuit DF.sub.1 inputs the output signal of the non-linear element 11 shown in FIG. 5, whereas the subtractor 13 inputs the output signal of the delay circuit DR.sub.n.
J.sub.1, J.sub.2 in FIG. 9 designate junction circuits each simulating the scattering of compression wave which occurs at the portion of connecting two tube portions each having the different diameter in the resonance tube of the wind instrument. Herein, each junction circuit "J" is designed as "four-multiplication-grid" consisting of multipliers M.sub.1 to M.sub.4 and adders A.sub.1, A.sub.2. In the junction circuit, "1+kn", "-kn", "1-kn", "kn" designate coefficients which are multiplied by the input signals of the multipliers M.sub.1 to M.sub.4. These coefficients are determined in response to the signal scattering characteristic of the wind instrument. Then, the signal transmission is made by the junction circuits among the neighboring delay circuits. For example, the output signal of the delay circuit DF.sub.1 is sent to the delay circuit DF.sub.2 via the multiplier M.sub.1 in the junction circuit J.sub.1, while the output signal of the delay circuit DR.sub.n-1 is sent to the delay circuit DR.sub.n via the multiplier M3 in the junction circuit J.sub.1.
Instead of the above-mentioned junction circuit, the foregoing Japanese Patent Laid-Open Publication No. 63-40199 discloses the junction circuit designed by "three-multiplication-grid" as shown in FIG. 10. In FIG. 10, M.sub.5 to M.sub.7 designate multipliers, A.sub.3 to A.sub.5 designate adders and IV2 designates an inverter. In addition, "kn" designates a coefficient which is multiplied by the input signal of the multiplier M.sub.7. Similarly, "gm" and "1/gm" designate coefficients which are respectively multiplied by the multipliers M.sub.5, M.sub.6. Herein, the coefficient gm is determined by the following formula (5). EQU gm=[(1-kn)/(1+kn)].sup.0.5
By setting the coefficient as described above, the transmission gain is regulated.
In FIG. 9, TRM designates a terminal circuit which simulates the terminal portion 1E of the resonance tube 1. Herein, the output signal of the non-linear element 11 is passed through the delay circuits DF.sub.1 to DF.sub.n and junction circuits J.sub.1, J.sub.2 . . . and then supplied to the terminal circuit TRM. ML designates a multiplier which simulates the energy loss which is occurred when the compression wave is reflected by the terminal portion 1E. This multiplier ML multiplies the output signal of the delay circuit DF.sub.n by certain loss coefficient gl, and then the multiplication result is supplied to a phase inverter IV. This phase inverter IV simulates the phase inversion which is occurred between the reflected wave and progressive wave when the terminal portion 1E is not closed but opened. Therefore, when the terminal portion 1E is closed, the phase inverter IV is not required. Then, DC components of the output signal of the phase inverter IV is removed by DC removing circuit DCB. Thereafter, the output signal of the DC removing circuit DCB is supplied to the delay circuit DR.sub.1. This output signal is finally supplied to the adder 13 shown in FIG. 5 via the delay circuits DR.sub.n to DR.sub.1 and the junction circuits J.sub.2, J.sub.1, . . .
The sum of delay times of the delay circuits DF.sub.1 to DF.sub.n, DR.sub.1 to DR.sub.n is determined in response to the frequency of the musical tone to be sounded. Actually, the propagation velocity required when the progressive compression wave F propagates from the reed to the tube end portion coincides with the propagation velocity required when the reflected compression wave R propagates from the tube end portion to the reed in the wind instrument. For this reason, the circuit shown in FIG. 9 is designed such that the sum of delay times of the delay circuits DF.sub.1 to DF.sub.n is set equal to the sum of delay times of the delay circuits DR.sub.1 to DR.sub.n.
As described heretofore, the non-linear element 11 and resonance circuit 12 shown in FIG. 5 are designed by simulating several portions of the wind instrument. By using the circuit shown in FIG. 5, it is possible to synthesize the desirable wind instrument tone. In case of the string instrument such as the guitar other than the above-mentioned wind instrument, the non-linear element 11 is designed in response to the elastic characteristic of the string and the resonance circuit 12 is designed in response to the length of the string, by which the circuit shown in FIG. 5 can simulate the string instrument tone. Meanwhile, it is possible to make the reverberation effect applying apparatus by use of the above-mentioned resonance circuit, for example.
Meanwhile, in the case where the operation of the musical tone synthesizing apparatus is embodied by operational processes executed by signal processors, the conventional musical tone synthesizing apparatus uses the foregoing four-multiplication-grid or three-multiplication-grid as the junction circuit, which thereby increases the times of carrying out the multiplication in each junction circuit. Therefore, in order to embody the desirable signal processing speed, the conventional apparatus requires high processing ability for the signal processor, which raises a problem in that the circuit configuration must be complicated. Instead of the foregoing grid circuits to be used as the junction circuit, it is possible to use other circuits as various junction circuits having various transmission characteristics. In this case, it is possible to obtain the variation of the signal processings by varying the coefficient to be used in each multiplier included in the junction circuit.
Next, description will be given with respect to the conventional reverberation effect applying apparatus by referring to FIG. 11. In FIG. 11, SF.sub.1 to SF.sub.3, SR.sub.1 to SR.sub.3 designate shift registers each simulating the transmission delay of reverberation tone; IV1A to IV3A, IV1B to IV3B designate inverters; MA.sub.1 to MA.sub.3, MB.sub.1 to MB.sub.3 designate multipliers each simulating the attenuation of reverberation tone; and A1A to A3A, A1B to A3B, A123, B123 designate adders each simulating the convolution of the reverberation tones which are convoluted in the acoustic space. In addition, each of three pairs of the shift registers SF.sub.1, SR.sub.1 ; SF.sub.2, SR.sub.2 ; SF.sub.3, SR.sub.3 corresponds to the transmission path of one reverberation tone in the acoustic space. Further, the number of stages of each shift register (represented by numerals N.sub.1, N.sub.2, N.sub.3) is determined in response to the transmission delay time of the transmission path of reverberation tone to be simulated.
Next, description will be given with respect to the operation of the above-mentioned reverberation effect applying apparatus. In FIG. 11, the input signal corresponding to the musical tone is applied to the adder B123, and then the output of the adder B123 is supplied to the shift registers SF.sub.1, SF.sub.2, SF.sub.3 via the adders A1A, A2A, A3A respectively. The input signal of the shift register SF.sub.1 is delayed by the predetermined delay time and then inverted by the inverter IV1B. The output of the inverter IN1B is supplied to the shift register SR.sub.1 via the adder A1B, wherein it is delayed by the predetermined delay time in the shift register SR.sub.1. Thereafter, the output of the shift register SR.sub.1 is fed back to the adder A1A via the inverter IV1A. Thus, the loop consisting of these elements A1A, SF.sub.1, IV1B, A1B, SR.sub.1, IV1A simulates the reverberation tone which transmits forth and back in the transmission path. Similarly, other loops consisting of the shift registers SF.sub.2, SR.sub.2, SF.sub.3, SR.sub.3 etc. simulate other transmission paths.
Meanwhile, the outputs of the shift registers SF.sub.1, SF.sub.2, SF.sub.3 are multiplied by loss coefficients a.sub.1, a.sub.2, a.sub.3 in the multipliers MA.sub.1, MA.sub.2, MA.sub.3 respectively. Then, outputs of the multipliers MA.sub.1 to MA.sub.3 are added together in the adder A123. The output of the adder A123 is delivered to the adders A1B, A2B, A3B respectively. On the other hand, the outputs of the shift registers SR.sub.1, SR.sub.2, SR.sub.3 are multiplied by loss coefficients b.sub.1, b.sub.2, b.sub.3 in the multipliers MB.sub.1, MB.sub.2, MB.sub.3 respectively. Then, the outputs of the multipliers MB.sub.1 to MB.sub.3 are added together in the adder B123. The output of the adder B123 is delivered to the adders A1A, A2A, A3A respectively. Thus, the signal which propagates each shift register is attenuated, which simulates the attenuation of the reverberation tone. As a result, the adder A123 can output the musical tone to which the reverberation effect is applied.
Meanwhile, the foregoing musical tone synthesizing apparatus as shown in FIG. 9 provides the delay circuits DF.sub.1 to DF.sub.n for the progressive compression wave and other delay circuits DR.sub.1 to DR.sub.n for the reflected compression wave, wherein the delay times are set equal in both of DF and DR. Therefore, the number of the delay circuits to be provided must be increased in response to the kind of the musical tone to be simulated. This enlarges the hardware of the musical tone synthesizing apparatus. In addition, when the musical synthesizing operation is carried out by the operation of the signal processor, the times of accessing the memory must be increased. Further, the musical tone is not sounded until the output signal of the non-linear element passes through the delay circuits DF.sub.1 to DF.sub.n, which deteriorates the real-time operation of synthesizing the musical tone.
Lastly, FIG. 12 shows another conventional musical tone synthesizing apparatus which simulates the tone-generation mechanism of the wind instrument. In FIG. 12, 21 designates a read-only memory (ROM), 22 designates an adder, 23 designates a subtractor, and 24, 25, 26 designate multipliers, all of which configures an excitation circuit 20 which simulates the operations of mouth-piece and reed of the wind instrument such as the clarinet.
Next, description will be given with respect to stored information of the ROM 21. Of course, the wind instrument is performed by that the performer holds the mouth-piece in his mouth and then blows his breath into the gap between the mouth-piece and reed. In this case, the sectional area of the above-mentioned gap is varied in response to the sum of the air pressure in the gap and reed pressure (which is called "Embouchure" in French) applied to the reed when the performer holds the mouth-piece in his mouth. The relation between the whole pressure applied to the reed and the sectional area of the gap is set based on the elastic characteristic of the reed, so that non-linear relation will be established between them. The ROM 21 stores a non-linear function table representative of the relation between the reed pressure (i.e., input PP) applied to the reed and the sectional area (i.e., output S) of the gap. Herein, based on input data PP corresponding to the reed pressure to be used as the address, the output data S corresponding to the sectional area of gap can be read from the table.
27 in FIG. 12 designates a filter which simulates the transmission characteristic of the resonance tube of the wind instrument.
In FIG. 12, the subtractor 23 receives information P representative of the blowing pressure applied to the wind instrument and information q supplied from the filter 27. This information q corresponds to the compression wave which inversely flown into the mouth-piece from the tube of the wind instrument. The subtractor 23 subtracts the information q from the information P to thereby output information .DELTA.P representative of the pressure in the mouth-piece. Then, the adder 22 adds the information .DELTA.P with information E corresponding to the foregoing reed pressure applied to the reed when the performer holds the mouth-piece in his mouth. Thus, the adder 22 outputs information PP representative of the whole pressure applied to the reed. This information PP is supplied to the ROM 21.
Then, the ROM 21 outputs information S corresponding to the sectional area of gap to the multiplier 25. Meanwhile, the multiplier 24 multiplies the information .DELTA.P with "-1" to thereby output "-.DELTA.P" to the multiplier 25. Herein, the pressure information .DELTA.P represents the pressure of the progressive compression wave which directs from the reed into the tube, while "-.DELTA.P" represents the pressure of the reflected compression wave which directs from the tube end to the reed. Due to the multiplication carried out by the multiplier 24 by use of the multiplication coefficient "-1", the above-mentioned pressure information .DELTA.P is converted into -.DELTA.P. In the multiplier 25, the information S corresponding to the sectional area of the gap formed between the mouth-piece and reed is multiplied by the information -.DELTA.P corresponding to the gap pressure applied to the gap, so that multiplication result FL is obtained. This information FL corresponds to the flow velocity of the air-flow which passes through the gap.
Then, the multiplier 26 multiplies the above-mentioned information FL by information G representative of the flow-resistance which avoids the air-flow passing through the inlet of the tube (i.e., the portion near the reed-mounting-portion of the tube). Thus, the multiplier 26 outputs information X representative of the pressure of the progressive compression wave which progresses into the tube. This information X is supplied to the filter 27, from which the information q representative of the pressure of the air-flow which inversely flows toward the reed is outputted to the subtractor 23. Thereafter, as described before, the information X is obtained from the multiplier 26 and supplied to the filter 27.
As described heretofore, the information corresponding to the pressure of the air-flow is circulated in the closed-loop consisting of the excitation circuit 20 and filter 27. In short, the resonance operation is carried out in such closed-loop. Then, based on the musical tone information picked up from the predetermined node of the filter 27, the musical tone is to be generated.
The above-mentioned conventional musical tone synthesizing apparatus as shown in FIG. 12 is suitable to the wind instrument (such as the clarinet or saxophone) in which the reed movement depends on the pressure .DELTA.P at the gap formed between the mouth-piece and reed. However, such conventional apparatus cannot be applied to the brass instrument such as the trumpet which utilizes the performer's lip as the reed, wherein the performer's lip is called "lip reed". The reasons are described below.
In the case where the lip opening degree is relatively small when using the lip reed, the mouth-inside pressure forces the lip to open, while the air pressure applied from the tube (hereinafter, simply referred to as tube-side pressure) forces the lip to close. However, if the lip opening degree becomes relatively large, the tube-side pressure does not affect the lip movement anymore. In short, in case of the lip reed, when the mouth-inside pressure and tube-side pressure are varied, the lip opening degree must be varied even if the pressure difference between them is not changed. Therefore, it is not possible to directly determine the lip opening degree based on the pressure difference between the mouth-inside pressure and tube-side pressure. For this reason, there is a problem in that the conventional apparatus cannot synthesize the musical tone of the brass instrument.